In an oven-safe skillet, heat oil over medium-high heat. Add onions and saut until translucent, approximately 5-7 minutes. Add garlic and cook for an additional 2 minutes. Add sauerkraut and saut for 3 minutes. Add apples and brown sugar, stir to combine and cook for another 3-5 minutes. Add wine and transfer to oven to cook for 25 minutes. Season to taste with salt and pepper.

Grill hot dogs. Place grilled dogs buns and top with stone-ground mustard and some of the apple-sauerkraut mixture.